Lemma 2.1.7.
Let
Proof of 1:
A unital
Conversely, if
Then
set
Then
Reflection:
The first containment follows from continuity of the map.
The second relies on surjectivity, we have this decomposition of elements in
Proof 2:
Follows immediately from 1. and Lemma 2.1.5 (Whitehead).
[Insert detailed rumination]
Proof 3:
If